湍流模拟的困境
The dilemma of turbulence modelling
摘要：
本文介绍了强空间中Euler方程多重解的一种新构造方法，它揭示了在避免粘性极限构造的同时，与具有特殊力项的多重Navier斯托克斯方程解的关系。这表明，为了使Navier斯托克斯方程Cauchy问题的解唯一，必须对与不定常的外力项施加严格的限制.这种限制是在所谓的千年问题的声明中强加的。最小湍流模型应该包含较弱的力项，以考虑边界条件和力。然而，我们表明，最近提出的这种类型的模型，没有一个唯一的解决方案。模拟湍流模型缺乏确定性表明了一个困境：要么模型过于简单，无法捕获湍流，但可能具有唯一的光滑解，要么存在建模间隙，因为模型无法确定唯一的解。
英文摘要：
A new construction technique of multiple solutions of the Euler equa- tion in strong spaces is introduced which reveals the relationship to multi- ple Navier Stokes equation solutions with special force terms while avoid- ing viscosity limit constructions. This shows that severe restrictions have to be imposed on time dependent external force terms in order to ob- tain uniqueness for the Navier Stokes equation Cauchy problem. Such restrictions are imposed in the statement of the so-called millenium prob- lem. Minimal turbulence models should arguably incorporate weaker force terms in order to account for boundary conditions and forces. However, we show that models of this type which have been proposed recently, do not have a unique solution. This lack of determinism of mimimal turbu- lence models indicates a dilemma: either models are too simple to capture turbulence but may have unique smooth solutions, or there is a modelling gap as the model does not determine a unique solution.
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